Minimal state space realisation of continuous-time linear time-variant input–output models

ABSTRACT

In the linear time-invariant (LTI) framework, the transformation from an input–output equation into state space representation is well understood. Several canonical forms exist that realise the same dynamic behaviour. If the coefficients become time-varying however, the LTI transformation no longer holds. We prove by induction that there exists a closed-form expression for the observability canonical state space model, using binomial coefficients.

KEYWORDS:

• Time-varying systems
• realisation theory
• system identification

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the Fund for Scientific Research (FWO-Vlaanderen), by the Flemish Government (Methusalem Fund, METH1), and by the Belgian Federal Government (IUAP VII, DYSCO).